Heat the olive oil in a large pot over medium heat; cook the chicken in the hot oil until it has begun to brown. Add all the ingredients except the parsley to the pot. There should be enough liquid to just cover the vegetables. If not, add more chicken stock.
Bring the mixture to a simmer and cook, stirring occasionally, until the carrots are tender, about 30 minutes. Remove the bay leaves and garnish with the parsley to serve.